ztrans - Maple Help

MTM

 ztrans
 Z-transform

 Calling Sequence ztrans(M) ztrans(M,z) ztrans(M,n, z)

Parameters

 M - array or expression n - variable z - variable

Description

 • F = ztrans(f) is the Z-transform of the scalar f with default independent variable n.  If f is not a function of n, then f is  assumed to be a function of the independent variable returned by findsym(f,1). The default return is a function of z.
 • If f = f(z), then ztrans returns a function of w.
 • By definition, $F\left(z\right)=\sum _{n=0}^{\mathrm{\infty }}\frac{f\left(n\right)}{{z}^{n}}$ where the summation above proceeds with respect to z.
 • ztrans(f,w) makes f a function of the variable w instead of the default z.
 • ztrans(f,k,w) takes f to be a function of k instead of the default n. The summation is then with respect to w.
 • The ztrans(M) function computes the element-wise Z-transform of M.  The result, R, is formed as R[i,j] = ztrans(M[i,j], n,z).

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $\mathrm{ztrans}\left(\mathrm{sin}\left(\frac{\mathrm{\pi }}{2}n\right)\right)$
 $\frac{{z}}{{{z}}^{{2}}{+}{1}}$ (1)
 > $\mathrm{ztrans}\left(\mathrm{sin}\left(\frac{\mathrm{\pi }}{2}z\right)\right)$
 $\frac{{w}}{{{w}}^{{2}}{+}{1}}$ (2)
 > $\mathrm{ztrans}\left(\mathrm{sin}\left(\frac{\mathrm{\pi }}{2}n\right),s\right)$
 $\frac{{s}}{{{s}}^{{2}}{+}{1}}$ (3)
 > $\mathrm{ztrans}\left(k\mathrm{sin}\left(\frac{\mathrm{\pi }}{2}n\right),k,s\right)$
 $\frac{{\mathrm{sin}}{}\left(\frac{{\mathrm{\pi }}{}{n}}{{2}}\right){}{s}}{{\left({s}{-}{1}\right)}^{{2}}}$ (4)
 > $M≔\mathrm{Matrix}\left(\left[\mathrm{sin}\left(\frac{\mathrm{\pi }}{2}n\right),k\mathrm{sin}\left(\frac{\mathrm{\pi }}{2}n\right)\right]\right):$
 > $\mathrm{ztrans}\left(M\right)$
 $\left[\begin{array}{cc}\frac{{z}}{{{z}}^{{2}}{+}{1}}& \frac{{k}{}{z}}{{{z}}^{{2}}{+}{1}}\end{array}\right]$ (5)